Singular perturbation analysis (SPA) is a powerful tool, not only for approximating the solution of multiscale systems, but also for acquiring the most significant physical understanding. Physical processes in almost all scientific fields were treated by the various elegant methodologies of SPA. However, the application of SPA is limited by the size/complexity and the dimensionality of the model. The effort to systematize the various SPA methodologies lead to the introduction of the Geometric Singular Perturbation Analysis (GSPA), according to which we should focus on the dynamics that develop along the low dimensional surfaces that develop in phase space, on which nearby trajectories contract at an exponential rate along the normal (fast) directions and then move along these surfaces in the tangent (slow) directions. CSP is an algorithmic methodology developed in the GSPA spirit, so it is not hindered by the size/complexity or the dimensionality of the model and requires minimal input from the investigator. The history of its development will be briefly described and several applications in the fields of chemical kinetics and biology will be discussed.
After obtaining his PhD degree from the Mechanical and Aerospace Engineering Dept. of UCLA in 1986, Dr. Dimitris Goussis joined the Department of Mechanical and Aerospace Engineering at Princeton University as a Research Staff until 1991. He then returned to Greece, where he joined the faculty of the Mechanical Engineering Dept. at the University of Patras and then the faculty of the School of Applied Mathematical and Physical Sciences at the National Technical University of Athens. The summer of 2016 he joined the faculty of the Mechanical Engineering Department at Khalifa University in UAE.
The major focus of his work is the development of algorithmic methodologies for the acquisition of the essential physical understanding, by analyzing mathematical models that simulate physical phenomena, with applications in the fields of combustion, biology, pharmacokinetics and mechanics.